Mr.Rhett was not a military man, nor did he belong to the navy.

He was a citizen capable of commanding soldiers, and as such he went forth to destroy the pirate Thomas.
Mr.Rhett met people enough along the coast who told him where he might find the pirate, but he found no one to tell him how to navigate the dangerous waters of the Cape Fear River, and so it was that soon after entering that fine stream he and his consort found themselves aground.
Mr.Rhett was quite sure that he had discovered the lair of the big game he was looking for.

Just before dark, three boats, well filled with men, had appeared from up the river, and they had looked so formidable that everything had been made ready to resist an attack from them.

They retired, but every now and then during the night, when there was quiet for a few minutes, there would come down the river on the wind the sound of distant hammering and the noise of saws.
It was after midnight before the Henry and the Sea Nymph floated free, but they anchored where they were and waited for the morning.

Whether they would sail up the river after the pirate or whether he would come down to them, daylight would show.
Mr.Rhett's vessels had been at anchor for five hours, and every man on board of them were watching and waiting, when daylight appeared and showed them a tall ship, under full sail, rounding the distant headland up the river.